Let (M,g) be a \(C^{\infty}\) 4-dimensional Riemannian manifold. (M,g) is said to be a quaternionic manifold if the structural group O(4n) can be reduced to Sp(n)\(\cdot Sp(1)\). On such a manifold there is a globally defined 4-form \(\Omega\) [see V. Y. Kraines, Trans. Am. Math. Soc. 122, 357-367 (1966; Zbl 0148.161)]. If \(\nabla \Omega =0\) where \(\nabla\) is the Riemannian connection, then M is said to be a quaternionic Kähler manifold. In this paper, the authors establish some symmetry properties of \(\nabla \Omega\) and prove the following result (which may be compared with the corresponding one in dimension 2 for almost Hermitian manifolds): Let M be a 4-dimensional quaternionic manifold; then M is a Kähler quaternionic manifold.